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  2. Discrete logarithm - Wikipedia

    en.wikipedia.org/wiki/Discrete_logarithm

    It turns out that much internet traffic uses one of a handful of groups that are of order 1024 bits or less, e.g. cyclic groups with order of the Oakley primes specified in RFC 2409. [6] The Logjam attack used this vulnerability to compromise a variety of internet services that allowed the use of groups whose order was a 512-bit prime number ...

  3. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d. Derivations also use the log definitions x = b log b (x ...

  4. Binary logarithm - Wikipedia

    en.wikipedia.org/wiki/Binary_logarithm

    Every family of sets with n different sets has at least log 2 n elements in its union, with equality when the family is a power set. [30] Every partial cube with n vertices has isometric dimension at least log 2 n, and has at most ⁠ 1 / 2 ⁠ n log 2 n edges, with equality when the partial cube is a hypercube graph. [31]

  5. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.

  6. List of small groups - Wikipedia

    en.wikipedia.org/wiki/List_of_small_groups

    Dih n: the dihedral group of order 2n (often the notation D n or D 2n is used) K 4: the Klein four-group of order 4, same as Z 2 × Z 2 and Dih 2; D 2n: the dihedral group of order 2n, the same as Dih n (notation used in section List of small non-abelian groups) S n: the symmetric group of degree n, containing the n! permutations of n elements

  7. Index calculus algorithm - Wikipedia

    en.wikipedia.org/wiki/Index_calculus_algorithm

    It requires a factor base as input. This factor base is usually chosen to be the number −1 and the first r primes starting with 2. From the point of view of efficiency, we want this factor base to be small, but in order to solve the discrete log for a large group we require the factor base to be (relatively) large. In practical ...

  8. Find first set - Wikipedia

    en.wikipedia.org/wiki/Find_first_set

    The log base 2 can be used to anticipate whether a multiplication will overflow, since ⌈log 2 (xy)⌉ ≤ ⌈log 2 (x)⌉ + ⌈log 2 (y)⌉. [53] Count leading zeros and count trailing zeros can be used together to implement Gosper's loop-detection algorithm, [54] which can find the period of a function of finite range using limited resources ...

  9. Partial sorting - Wikipedia

    en.wikipedia.org/wiki/Partial_sorting

    A further relaxation requiring only a list of the k smallest elements, but without requiring that these be ordered, makes the problem equivalent to partition-based selection; the original partial sorting problem can be solved by such a selection algorithm to obtain an array where the first k elements are the k smallest, and sorting these, at a total cost of O(n + k log k) operations.